Algebra of frontier points via semi-kernels

Jiarul Hoque; Shyamapada Modak

doi:10.17776/csj.784074

EN

Algebra of frontier points via semi-kernels

Abstract

In topological spaces, the study of interior and closure of a set are renowned concepts where the interior is defined as the union of open sets and the closure is defined as the intersection of closed sets. In literature, it is also a significant study while a set is defined as the intersection of open sets, and the union of closed sets. These respective ideas are known as the kernel of a set and its complementary function. Utilizing these ideas, some authors have introduced various kinds of results in topological spaces. Some mathematicians have extended these concepts via Levine’s semi-open sets to semi-kernel and its complementary function. The study of these notions is also a remarkable part of the field of topological spaces as the collection of semi-open sets does not form a topology again. In this paper, we have taken the semi-kernel and its complementary function into account to introduce new types of frontier points. After that we have studied and presented several characterizations of these new types of frontiers and established relationships among them. Finally, we have shown that semi-homeomorphic images of these new types of frontiers are invariant.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Jiarul Hoque
0000-0003-1055-9820
India

Shyamapada Modak ^*
0000-0002-0226-2392
India

Publication Date

June 30, 2021

Submission Date

August 22, 2020

Acceptance Date

May 31, 2021

Published in Issue

Year 2021 Volume: 42 Number: 2

DOI

https://doi.org/10.17776/csj.784074

IZ

https://izlik.org/JA33PY93SM

Cite

RIS / Bibtex

APA

Hoque, J., & Modak, S. (2021). Algebra of frontier points via semi-kernels. Cumhuriyet Science Journal, 42(2), 339-345. https://doi.org/10.17776/csj.784074

Öz

Algebra of frontier points via semi-kernels

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite